544 research outputs found
New Partition Identities From -Modules
In this paper we conjecture combinatorial Rogers-Ramanujan type colored
partition identities related to standard representations of the affine Lie
algebra of type , , and we conjecture similar colored
partition identities with no obvious connection to representation theory of
affine Lie algebras.Comment: 19 page
Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
This is the first in a series of papers in which we study vertex-algebraic
structure of Feigin-Stoyanovsky's principal subspaces associated to standard
modules for both untwisted and twisted affine Lie algebras. A key idea is to
prove suitable presentations of principal subspaces, without using bases or
even ``small'' spanning sets of these spaces. In this paper we prove
presentations of the principal subspaces of the basic A_1^(1)-modules. These
convenient presentations were previously used in work of
Capparelli-Lepowsky-Milas for the purpose of obtaining the classical
Rogers-Ramanujan recursion for the graded dimensions of the principal
subspaces.Comment: 20 pages. To appear in International J. of Mat
Constructing quantum vertex algebras
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over \C, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over \C[[h]]) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
\C, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a family of quantum vertex algebras closely related
to Zamolodchikov-Faddeev algebras.Comment: 37 page
Tutorial in oral antithrombotic therapy: Biology and dental implications
Objectives: Recent developments of new direct oral anticoagulants that target specific clotting factors necessitate
understanding of coagulation biology. The objective of this tutorial is to offer dental
professionals a review of
coagulation mechanisms and the
pharmacodynamics of the conventional and new oral anticoagulants. Also, we
summarized the dental implications of the conventional and new anticoagulants.
Method
: We searched Medline using search terms "antithrombotic", "antihemostasis" or "anticoagulation" and
combined them with the search results of "dental", "oral surgery" or "periodontal". We restricted the results to
"human" and "English".
Results: The early coagulation cascade, the new cell-based coagulation model, the
pharmacokinetics and
pharmacodynamics of conventional antithrombotics, and new oral anticoagulants were reviewed. The new direct factor
Xa inhibitors and the direct thrombin inhibitor (s), called direct oral anticoagulants (DOAs) have rapid onset of
action, fast elimination on cessation, and fewer drug-drug or drug-food interactions than warfarin. However, the
lack of antidotes raises concerns that some dental
procedures may trigger serious hemorrhagic events. Additionally, careful
perioperative withdrawal and resumption
protocols for the DOAs are reviewed, because DOAs' blood
levels are dependent on renal function. Also, various reversal strategies in the event of excessive bleedings are
summarized. Perioperative management of dental
patients taking new DOAs and conventional oral anticoagulants
are also discussed. However, the
perioperative strategies for DOAs are yet to be validated in randomized trials
Fusion rules and complete reducibility of certain modules for affine Lie algebras
We develop a new method for obtaining branching rules for affine Kac-Moody
Lie algebras at negative integer levels. This method uses fusion rules for
vertex operator algebras of affine type. We prove that an infinite family of
ordinary modules for affine vertex algebra of type A investigated in Adamovi\'c
and O. Per\v{s}e (2008) is closed under fusion. Then we apply these fusion
rules on explicit bosonic realization of level -1 modules for the affine Lie
algebra of type , obtain a new proof of complete reducibility
for these representations, and the corresponding decomposition for . We also obtain the complete reducibility of the associated level -1 modules
for affine Lie algebra of type . Next we notice that the
category of modules at level obtained in
Per\v{s}e (2012) has the isomorphic fusion algebra. This enables us to
decompose certain and --modules at negative levels.Comment: 18 pages; final version, to appear in Journal of Algebra and Its
Application
The structure of parafermion vertex operator algebras
It is proved that the parafermion vertex operator algebra associated to the
irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of
level k coincides with a certain W-algebra. In particular, a set of generators
for the parafermion vertex operator algebra is determined.Comment: 12 page
The N=1 triplet vertex operator superalgebras
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras
SW(m), , which are natural super analogs of the triplet vertex
algebra family W(p), , important in logarithmic conformal field
theory. We classify irreducible SW(m)-modules and discuss logarithmic modules.
We also compute bosonic and fermionic formulas of irreducible SW(m) characters.
Finally, we contemplate possible connections between the category of
SW(m)-modules and the category of modules for the quantum group
U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on
properties of characters and the Zhu's algebra A(SW(m)). This paper is a
continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version,
to appear in CM
The subconvexity problem for \GL_{2}
Generalizing and unifying prior results, we solve the subconvexity problem
for the -functions of \GL_{1} and \GL_{2} automorphic representations
over a fixed number field, uniformly in all aspects. A novel feature of the
present method is the softness of our arguments; this is largely due to a
consistent use of canonically normalized period relations, such as those
supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References
updated
Gastric atrophy and oesophageal squamous cell carcinoma: Possible interaction with dental health and oral hygiene habit
Background:Gastric fundal atrophy has been hypothesised to increase the risk of oesophageal squamous cell carcinoma (OSCC), but studies have shown inconsistent results.Methods:We measured serum pepsinogen I (PGI) and pepsinogen II (PGII) among 293 incident cases and 524 matched neighbourhood controls in a high-risk area of Northern Iran. Conditional logistic regression model was used to estimate odds ratios (ORs) and their 95% confidence intervals (CIs).Results:After controlling for age, sex, residence area and other potential confounders, gastric atrophy (defined by a validated criterion, PGI <55 μg dl-1) was associated with a two-fold increased risk (OR=2.01, 95% CI: 1.18, 3.45) of OSCC in the absence of nonatrophic pangastritis (defined as PGII <11.8 μg dl-1). Stratification by PGII decreased the misclassification errors due to cancer-induced gastritis. Presence of both poor dental health, indicated by higher than median sum of decayed, missing, and filled teeth (DMFT score), and gastric atrophy further increased the risk of OSCC (OR=4.15, 95% CI: 2.04, 8.42) with relative excess risk due to interaction (RERI) of 1.47 (95% CI: 1.15, 4.1). Coexistence of poor oral hygiene habit with gastric atrophy elevated OSCC risk eight times (OR=8.65, 95% CI: 3.65, 20.46) and the additive interaction index was marginally statistically significant (RERI=4.34, 95% CI: 1.07, 9.76).Conclusion:Gastric atrophy is a risk factor for OSCC, and poor dental health and oral hygiene habit may act synergistically in increasing the risk. © 2012 Cancer Research UK
Granulomatous cheilitis associated with exacerbations of Crohn's disease: a case report
<p>Abstract</p> <p>Introduction</p> <p>Crohn's disease is a disease involving the whole gastrointestinal tract from the mouth to the anus. Oral lesions are considered to be an important extraintestinal manifestation. Granulomatous cheilitis has been recognized as an early manifestation of Crohn's disease. It may follow, coincide with or precede the onset of Crohn's disease. The aim of this presentation is to describe a rare case of a patient with Crohn's disease in whom significant swelling of the lower lip not only preceded the diagnosis of Crohn's disease for two years, but it manifested as an early clinical index of the recurrence of the intestinal disease as well.</p> <p>Case presentation</p> <p>A man aged 25 was admitted in our department on August 1999 with chronic diarrhea and loss of weight. His bowel symptoms started in 1998 at the age of 24. However, two years previously (June 1996) he noticed a swelling of the lower lip, which contrasted significantly with the previously normal appearance of his mouth. A lip biopsy performed at that time was compatible with granulomatous cheilitis. Crohn's disease involving the terminal ileum and large bowel was diagnosed in 1998 and confirmed on the basis of colonoscopy, enteroclysis and histology findings of the small and large bowel. Conservative treatment resulted in clinical and laboratory improvement of the bowel symptoms and lip swelling. During the following years the disease was active with exacerbations and remissions of mild to moderate severity. The swelling of the lower lip occurred in parallel with the exacerbations of the bowel disease, returning to normal during periods of remission.</p> <p>Conclusion</p> <p>Significant swelling of the lower lip due to granulomatous cheilitis could be the first manifestation of Crohn's disease, preceding intestinal symptoms. Exacerbation of the lip lesion could be an early clinical sign of a relapse of the underlying intestinal disease.</p
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